Resolution setting for 32 inch LCD TV as a PC monitor
Solution 1:
The answer is fairly simple, but not always easy to explain. The highest resolution your TV supports is 720p (1360x768). Your video card (great card, card is not an issue) can support much higher resolutions, but has detected the highest resolution of your TV and therefore limited the settings to 1360x768, which is the best resolution your TV can display perfectly.
Anything higher would NOT make the picture better (since the number of pixels is limited by the TV hardware / screen) but it could (and would) make it worse since a resolution that is not an exact multiple of the hardware resolution would force a conversion that would sacrifice clarity for completeness.
Imagine trying to display a picture of the letter "T" with only 4 pixels. You would either wind up with two black on top and two white on bottom, or four black, or three black and one white. In any case, the "T" would not look like a "T", and would instead look like a dash or a square or an upside down "L". You could, however, display a "T" easily with 9 pixels (three black across the top row, one black in the middle position in the second row, and one black in the middle position in the third row).
As you increase the resolution, items on the screen get smaller, so the "T" would eventually get so small that there would only be 4 pixels trying to display it, resulting in an unreadable letter. Now imagine that with a face in a crowd, or the detail of a photo. Things start to look worse, not better, as the resolution increases beyond what the hardware can support.
My advice to you is to either stick with 1360x768, which is the absolute best your TV can do based on the laws of physics, or get a monitor or TV that can support a higher resolution.
Solution 2:
LCDs generally tend to best run at a fixed resolution - which is the native resolution of the screen, and 1360x786 is a common one for '720P' screens. As long as your video card and system detected it properly, that should be the native resolution for the screen in question.
Video cards easily handle 1920x1080 or full HD, so with the latest drivers, your graphics card and driver shouldn't be the issue.
If its a full HD screen, playing around with your connection methods (HDMI is best, failing which DVI failing which VGA and so on) might help